1. Field of the Invention
The invention relates to a method of forming a 3D image of an object to be examined by:combining at least two reconstruction images. The invention also relates to an X-ray device which is particularly suitable for carrying out such a method.
2. Description of the Related Art
It is known to utilize two-dimensional projections of an object to be examined for the formation of a reconstruction image of the object to be examined; such projections have been acquired by means of an imaging system, for example an X-ray device such as a C-arm X-ray device, a computed tomography apparatus, a magnetic resonance tomography apparatus or an ultrasound device. Various reconstruction methods that utilize different algorithms, for example, the Feldkamp algorithm, are known for the reconstruction. They enable the formation of a reconstruction image of an object to be examined from two-dimensional projections acquired along a circular trajectory of the measuring device, that is, for example the X-ray source and the X-ray detector, around the object to be examined. However, this type of data acquisition usually does not provide adequate data for the inverse problem, that is, the reconstruction of a complete three-dimensional reconstruction image; this becomes apparent in particular in the so-called Radon space. For example, a data acquisition along a circular trajectory provides data only within a torus in the Radon space; this does not suffice for the formation of an exact three-dimensional reconstruction image for which data would be required within a complete sphere in the Radon space. Therefore, the Feldkamp algorithm is merely an approximation and yields a reconstruction image which is exact in the central layer whereas induced artifacts increase continuously as the distance from the central layer increases.
Granted, it is possible to mitigate this problem by combining data acquired along two or more trajectories. For example, from EP 860 696 A2 it is known to acquire projections along two semi-circular trajectories that extend at an angle of 60xc2x0 relative to one another, to form a respective reconstruction image from the projections acquired alone each time one trajectory, and to add the two reconstruction images subsequently so as to form a 3D image. The image quality can thus be improved, but artifacts still occur in the 3D image.
Therefore, it is an object of the invention to provide a method and an X-ray device for forming a 3D image of an object to be examined while improving the image quality.
This object is achieved. by means of a method in which at least two reconstruction images are combined by weighted addition, each reconstruction image being weighted with a weighting function which describes at least approximately the distribution of noise and/or artifacts in the reconstruction image, and by means of an X-ray device including an X-ray source and an X-ray detector that are rotatable about the object to be examined in order to acquire projections from different X-ray positions. The X-ray device also includes a reconstruction unit for forming reconstruction images from respective sets of projections acquired along different trajectories. In the X-ray device, a processor forms a 3D image of the object by combining at least two reconstruction images by weighted addition, each reconstruction image being weighted by a weighting function that describes at least approximately the distribution of noise and/or artifacts in the reconstruction image.
The invention is based on the recognition of the fact that noise and artifacts occurring in the reconstruction image are transferred to the resultant 3D image when two or more reconstruction images are simply added. The noise is due essentially to the hardware used, in particular the detector elements used, for example the X-ray detector, whereas the cause of the artifacts lies mainly in the fact that not all data necessary for an exact reconstruction can be acquired from projections acquired alone, a trajectory. Depending on the reconstruction algorithm used, a different type of noise and different artifacts are thus induced in a reconstruction image. In order to reduce the transfer of such noise or such artifacts from a reconstruction image to a resultant 3D image, the invention proposes to determine a weighting function for each reconstruction image, which weighting function at least approximately describes the distribution of noise and/or artifacts in the reconstruction image, to multiply the reconstruction image by the weighting function, and to add all reconstruction images thus weighted so as to form a resultant 3D image only after that.
In preferred further versions of the method in accordance with the invention the weighting functions are determined by simulations or measurements performed on a phantom object, or use is made of mathematical functions, for example functions which descend linearly or as a square root (or vary otherwise), for example, from the center to the edge of the reconstruction image to be weighted by the respective weighting function. The image quality of the resultant 3D image can be significantly improved in comparison with the known method even while using such simple mathematical functions as weighting functions.
Further improvements still can be achieved when the weighting function is adapted as accurately as possible to the distribution of the noise or the distribution of artifacts occurring in a reconstruction image. It may be arranged such that for each pixel or group of pixels of a reconstruction image there is assigned a value of the associated weighting function, so that each pixel or each croup of pixels can be individually weighted in dependence on the magnitude of the noise component or artifact component of this pixel or this group of pixels.
In a particularly attractive version of the methods the weighting functions are chosen in such a manner that artifacts and noise are separately weighted for each pixel or each group of pixels of a reconstruction image. This enables advantageous selection of the preferred type of disturbance and the location in the 3D image in which such disturbances are to be suppressed.
The invention is used particularly advantageously in an X-ray device that is provided with an X-ray source that generates a conical X-ray beam and with a two-dimensional X-ray detector, the X-ray source and the X-ray detector rotating about the object to be examined in order to acquire the projections. The X-ray device may be, for example, a C-arm X-ray unit. In principle, however, the invention can also be used in a computed tomography apparatus.